Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
594 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #324×D89 | C2 | semidirect |
| 3. #26018185 | C2 | semidirect |
| 4. #26018184 | C2 | semidirect |
| 5. C89×#1318 | C2 | semidirect |
| 22. C2×#13083573 | C8 | semidirect |
| 52. C2×Dic178 | C2×C8 | semidirect |
| 82. C2×D4×C89 | C2×C8 | semidirect |
| 168. #1318 | D89 | semidirect |
| 169. C89 | #11432 | semidirect |
| 224. C2×D4 | C8×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022842 | 2 |
| #324×D89 | 2 |
| #26018185 | 2 |
| #26018184 | 2 |
| C89×#1318 | 2 |
| #11432 | 89 |